Answer: Yes, the second day has more variability than the first day.
Step-by-step explanation:
Day 1: 5.0 4.8 5.1 5.1 4.8 5.1 4.8 4.8 5.0 5.2 4.9 4.9 5.0
Day 2: 5.8 4.7 4.7 4.9 5.1 4.9 5.4 5.3 5.3 4.8 5.7 5.1 5.7
Day 3: 6.3 4.7 5.1 5.9 5.1 5.9 4.7 6.0 5.3 4.9 5.7 5.3 5.6
The variability is related to the standard deviation, so we need to compare the standar deviation of the second day with the standard deviation of the first day.
The standard deviation can be calculated with a scientific calculator, and the method will depend on the one you are using.
Now, we also could do it by hand:
S = √( (1/(N-1))*∑(xₙ - xm)^2)
where N is the number of points (13 in both days), xm is the mean of the set and xₙ is each point of the set:
the means for both sets are:
xm1 = 4.9615
xm2 = 5.1846
S1 = 0.1387
S2 = 0.3848
Here we can see that the standard deviation in the second day is bigger, this would mean that the second distribution is less "thight" than the first one, so the second day has more variability than the first day.
